Actually it’s exactly the same. Both have a gap of about 20 years between the actual event and the story, some folks may recall it which makes the story feel more real, and it helps anchor the story.
Or, as the man said, sometimes a cigar is just a cigar.
That part of the Godfather was set in the 1950’s, even if Puzo wrote it in the late 60’s, so it was pertinent to highlight the story about how Sinatra got the part at that time.
I rifled through HOUSE OF CARDS and found the episode — the one in question is actually the 2nd season.
And it remains curious they spent screen time to defend Bush 22 years later— with real specificity — considering how the show slams Tea Party other times.